The PMU measurements used in this study are obtained from simulations and are thus noise free. However, in practice, PMU measurements are contaminated by noise. Hence, the sensitivities of the HGAN-based TSA method to noisy PMU measurements are analyzed. Following the study in [1]},
and [2]}, white Gaussian noise is added to the simulated PMU data. Four different signal-to-noise ratios (SNR), namely, 50dB, 60dB, 70dB, and 80dB, are considered. The classification accuracies of the HGAN-based method under different noise conditions are presented in Fig. REF . The classification results in Fig. REF  show that the noise mainly affects the performance of GAN 1. Larger noise will lead to a lower classification accuracy in GAN 1. However, it is observed that the classification accuracy of GAN 2 and GAN 3 are above 99%, and are not impacted by the addition of noise.
Another interesting observation is that among the five different noise conditions, GAN 1 achieves the highest classification accuracy when a noise of 80dB SNR is added to the measurements. This accuracy is even higher than using clean PMU data. This observation can be explained by the known fact that adding a small noise to the input data leads to a better performance of the GAN models, as they learn more general features of the transient data for a better classification performance [3]}.
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